To update and improve the ephemeris of G 9-40 b since its initial discovery, we first model all the available transit photometry using juliet. For the transiting planet, we followed the \(r_1\) , \(r_2\)  mathematical parametrization introduced by [1]} to fit the planet-to-star radius ratio \(p=R_p/R_*\)  and the impact parameter of the orbit \(b\) . We fit the stellar density (\(\rho _\star \) ) rather than the scaled semi-major axis (\(a/R_\star \) ) using an informed normal prior based on the stellar parameters from Table REF . The TESS and K2 data are modeled with a quadratic limb darkening law (shared among sectors for TESS), while the ground-based data were modeled with linear limb darkening laws, both parametrized with the uniform sampling scheme of [2]}. Using a quadratic and a linear limb darkening law is the recommended approach by [3]} when dealing simultaneously with space- and ground-based photometry. Each instrument is modeled including an additional jitter term and fixing the dilution factor (i.e., the amount that a light curve is diluted due to neighboring stellar contamination) to one due to the absence of nearby companions as shown in Sect. REF . Finally, to remove the stellar variability in the K2 light curve (Fig. REF ), we used the exponential GP kernel from celerite [4]}
\(k_{i,j} = \sigma ^2_\mathrm {GP,K2} \exp \left(- |t_i - t_j|/T_\mathrm {GP,K2}\right),\) 
